The present invention relates to digital doppler processors, in general, and more particularly, to a method and system for compensating the doppler processor for unbalance in the in-phase I and quadrature Q input signals thereof, and a sensing system for measuring the uncompensated unbalance in the I and Q signal inputs.
Digital doppler filters, such as an N-pulse digital filter, for example, are generally included in a digital doppler processor to process I and Q input signals to produce complex output signals X+jY which may be represented by a summation of a weighted set of the complex input signals. Generally, simplicity dictates creation of pairs of doppler filters having mirror-image frequency responses which may be exemplified by equation (1) below: ##EQU1## where A.sub.n .+-.jB.sub.n is representative of a set of complex weighting coefficients which create a pair of filters with mirror-image responses: the gain of the filter generated by weight set A.sub.n +jB.sub.n to doppler frequency +f is identical to the gain of the filter generated by weight set A.sub.n -jB.sub.n to doppler frequency -f.
However, practically, digital doppler filters process in-phase I and quadrature Q input signals having unbalanced gain and non-zero bias. The resulting complex distorted outputs X+jY may be exemplified by equation (2), found below: ##EQU2## where the gain unbalance k is defined as k.sup.2 =(I/Q), and I and Q represent the real and imaginary components of the input bias error, respectively. In addition, the weighting vector of the digital doppler filter may be defined in relation to the gain unbalance of the filter inputs as follows: ##EQU3## Accordingly, the filter output may be expressed as: ##EQU4##
Practical implementations of digital doppler filters having compensation systems to correct for errors in the I and Q input signals are exemplified in the following references:
1. F. E. Churchill et al., "The Correction of I and Q Errors in a Coherent Processor", IEEE Transactions AES-17, No. 1, January 1981, pages 131-136; PA1 2. U.S. Pat. No. 3,950,750, entitled "Radar System Having Quadrature Phase Detector Compensator", issued to F. E. Churchill et al., on Apr. 13, 1976; PA1 3. U.S. Pat. No. 4,003,054, entitled "Method of Compensating for Imbalances in a Quadrature Demodulator", issued to B. J. Goldstone on Jan. 11, 1977; and PA1 4. U.S. Pat. No. 4,122,448, entitled "Automatic Phase and Gain Balance Controller for a Base Band Processor", issued to R. G. Martin on Oct. 24, 1978.
These prior systems, especially the ones described in the aforementioned references to Churchill et al. are operative in a radar receiver to correct radar echo I and Q signals detected at the output of a set of analog-to-digital (A/D) converters of the receiver, based on measured unbalance in the gain and phase relationship of the I and Q signals. The Churchill compensation includes two multiplications and an addition which are performed at the high data sampling rate of the A/D converter, typically on the order of several megahertz. Accordingly, the corrected I and Q signals contain many more digital bits than their corresponding uncorrected digitized signals at the output of the A/D converter. Generally, a portion of the bits of least significance of the corrected I and Q input signals are discarded by truncation and/or round-off operations. (Refer to FIG. 3 of the aforementioned referenced patent 3,950,750). It should be noted that the multipliers and adders of the compensation implementation may be either specific hardware elements dedicated to these tasks or arithmetic steps performed by a digital computer. The culmination of these operations effect compensated input data for the doppler-filtering processes of the radar, for example.
In either implementation, these arithmetic operations increase cost, and the truncation of their resulting outputs may degrade performance. For example, while truncations or round-off generally have no significant effect on signals in the pass band of the subsequent doppler-filter operations, they can cause very serious degradation of the ability of the doppler-filter to suppress interference within its rejection frequency band. In addition, the truncations and/or round-offs may also distort the statistical character of noise, affecting the ability of subsequent processing in a radar, for example, to maintain control of false alarm rate. It has been found that by avoiding truncation operations, the degradation of the ability to suppress ground clutter and to maintain control of false alarm rate as the noise level of the input signalling varies may be ameliorated.
More specifically, in a radar application, a doppler filter processor generally operates to suppress two types of interference: ground clutter and rain (or chaff) clutter. Ground clutter, for example, comprises very strong radar echoes from terrain with a narrow doppler spectrum created by antenna scanning or foliage motion in the wind, centered at zero doppler frequency. On the other hand, radar reception from rain clutter is generally less intense but has a wider spectrum created by wind shear, centered at a doppler frequency corresponding to the mean radial wind speed. The ability of a digital doppler filter processor to suppress rain clutter is degraded by unbalance in the gain or phase of the I and Q input signals. FIG. 1 illustrates the effect of a 4% (I/Q) gain unbalance on the doppler side lobes of a typical doppler filter, before and after compensation. Note that the level of the worst doppler side lobe determines the suppression of rain or chaff relative to noise under the worst wind conditions; so, the ability to maintain low side lobes is of vital importance.
Although the ability to suppress ground clutter is not directly degraded by I and Q signal unbalance, the processes to compensate for this unbalance, however, can indirectly produce serious degradation by increasing the extent of distortions especially caused by truncation. Thus, it is particularly desirable to provide a solution which achieves the necessary compensation of the I and Q signal unbalance without the usual degradation of the ground clutter rejection capability.
In addition, the aforementioned references are also directed to methods of sensing the magnitude of gain and phase unbalance in the I and Q input signals to the digital doppler filters. The objective of these type sensors in general is to provide the necessary correction data at minimum cost. However, most of these type sensors impose certain constrains in order to reduce the number of costly mathematical operations, particularly multiplications and additions; but these constraints introduce problems.
For example, the sensor of U.S. Pat. No. 4,122,448 depends upon sampling a pure doppler test tone during "dead time", when its radar receiver is not occupied processing radar echoes. Since the interpulse period of the radar is generally variable, the phase of the test tone at the time of sampling is a parameter of concern. This particular reference teaches a sensor which requires precisely 0.degree.,90.degree., 180.degree. and 270.degree. phase conditions at successive samples of the injected test tone, a condition that is rarely possible to achieve. Other systems may require the phase change between successive samples to be very small, but this very low doppler test tone is difficult to generate to the required degree of purity.
The sensor directed to in the Churchill references eliminates the constraint on the phase of the injected test tone at the time of sampling, requiring only a precise test tone frequency. However, it achieves this relaxation by requiring six multiples and two divides (refer to equations 30 and 31 of the aforementioned paper to Churchill et al.), as well as sundry additions and subtractions. On the other hand, the Churchill sensing system is more tolerant of small distortions in the A/D conversions than the other sensing systems, because unbalance may be estimated from a large number of data samples with different phase conditions. That is, random errors tend to be reduced by averaging.
In summary, all of the aforementioned methods and systems for measuring and compensating for the I and Q signal unbalances have drawbacks which prevent their widespread application. While the Churchill et al. method and system is the most generally useful, it, however, is incompatible with pulse-to-pulse changes of interpulse period and is the most costly because of the required multiplications, divisions, and additions. The disclosed method and system found herebelow proposes to overcome these deficiencies.